Entry-level DSO's tend to exaggerate noise, since they can only show one intensity. A CRT does some sort of intensity grading, random noise tends to be darker than the stable signal, so you hardly see it. More expensive scopes try to emulate this behavior, but the Rigol will just show you the last signal at a constant intensity. It's also possible that the Rigol front-end produces more noise, since the HP was probably higher-end when it was new.
This persistance mode can only work on repetitive signals; it can't work on single sweep. However, on single sweeps the noise just sits there; it doesn't dance around attracting your attention like it does on repetitive sweep.
This is a dubious "feature", more gimmick, or even bug, than feature. Although it can be useful sometimes, its primary effect, particularly if defaulted to on, is to make the scope superficially appear more accurate while actually making it less accurate. Showing you the noise in your signal can be just as important as showing the intended signal. Sometimes you want to clean up the signal but this should be done at your explicit request, after you have seen the noise, rather than hiding the noise. I have spent a lot of time extracting small signals from large amounts of noise; there is a place for cleaned up signals.
The Rigol does have an infinite persistance mode (:DISPlay:PERSist), where each pixel, once written remains visible, though at a reduced intensity compared to the current refresh. This has roughly the opposite effect as the form of persistance described above as it actually highlights noise; this is likely to be more useful. It does not have exponential decay which would give the gimmick effect, though that ought to be easy to add.
The rigol has an averaging mode, where multiple sweeps are averaged together. When you want to clean up the signal and hide the noise, this is more genuinely useful than the phosphor gimick. It is vector rather than raster based, so the high resolution data sent to the computer is cleaned up and measurements made on the oscilloscope or on the computer can use the cleaned up data. In addition, it has filter modes that operate on the waveform (:CHANnel1:FILTer). The Rigol does have a switchable 20Mhz bandwidth limit (:CHANNEL1:BWLIMIT) on the input channels which can suppress high frequency noise which may be outside the frequency response of your circuity, anyway. Thus, when you do need to clean your data (preferably after inspecting the uncleaned data, first), you have several ways to do so.
One use for persistance is when using the scope as an XY display, such as when displaying
simulated laser show effects. However, the Rigol lacks a Z axis modulation input. Analog modulation would require an additional expensive high speed A/D converter channel, though it would be a zero marginal cost feature on a 4 channel scope. Digital (on/off) modulation, however, could employ the trigger input on the scope. It just takes some extra bits in memory; the memory on many fpga's is organized in multiples of 9 bits wide vs 8 bits wide so the extra bits may be free. Thus digital modulation should be a zero marginal cost upgrade on the 2 channel models.
Some noise might be an artifact of overclocking the A/D converters. One of the differences of the higher graded parts is that they might actually settle to within noise specs in the shorter alloted time available at 100Mhz vs 40Mhz. On more sluggish parts that don't make the grade, the signal may not have fully settled and may be between two A/D counts. While 1 count of noise is unavoidable as a signal may hover on the boundary between two counts effectively producing a very high noise gain, settling effects might not be consistent from sweep to sweep.
The Rigol doesn't antialias lines which can produce jagged edges on diagonal lines which are inherent on rasterized displays without antialiasing. It does appear as if it usually displays the trace by plotting two pixels vertically instead of one, but not always. This may happen when the 256 counts are reduced to somewhat less vertical pixels as a way of displaying intermediate values beyond the display resolution. This may make the noise appear a little more subdued but may also make it appear like there is 1 pixel of additional noise when you scrutinize the display.
A significant source of noise can be pickup in the probe. If you clip the probe ground lead to the tip, you have created a loop antenna which picks up noise from the surroundings. For illustration purposes, If you set this loop on top of the scope (inside the area occupied by the handle), you will see some some very significant noise from the scope itself at 2mV per division. Now, hold the clip and rotate the probe 180 degrees about its axis. This changes the ground lead from a loop to a figure 8, which like a twisted pair produces some cancelling. Even in such close proximity to the noise source, this drops the noise by more than half. Of course, you can also appear to get the opposite effect if you start in a less noisy area and rotate half the loop into the noisy area, so keep the loop(s) centered on the same area.
Emulating the persistance/brightness defects of an analog scope is a lot like tube vs transistor amplifiers. You can emulate the poorer fidelity of a tube amplifier on a solid state amplifier with a handfull of components, but only an Audiophool would argue that the tube amplifier is superior. You can give people a choice if they prefer a distorted aesthetic, just as you can blur a high quality image for a particular aesthetic but a camera which can only produce blurred images is inferior. Choice is good, locking people into bad choices or defaulting them to on so they bite the unwary, is bad.
Most of the noise on the scope at logic level scales is +/-1 count. At the 2mv/div level, it is noticeably higher but not that different from my Tektronix 2236 Analog Oscilloscope, which cost about $3500 when I bought it new or about $9700 in todays dollars. On 2mV per division (and 500uS) with a looped probe, most of the noise is within about 2 minor divisions (plus a few spikes) on the Rigol and a little over 1 on the Tektronix, using the Rigol probe on 1x in both cases, though a good portion of that difference may be the analog scope hiding the noise. With foil shorting the probe tip to the ground ring or with the probes disconnected, both scopes show about 1 minor division of noise. It is more noticable on the Rigol, but it isn't really worse. This is with a fan, a computer, two LCD monitors, a cell phone, a WiFi router, a DSL modem, a gigabit ethernet switch, a laser printer and an injet printer/scanner, a barcode printer, a DVD recorder, a couple compact fluorescent light bulbs, a keyboard and mouse, a laptop, an air conditioner, assorted cables, and two oscilloscopes making noise in the immediate vicinity. However, outside RF is significantly attenuated.
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